NEW YORK (CNN) -- Saying it has exhausted all DNA technology, the New York City Medical Examiner has halted the process of identifying human remains from the September 11, 2001, terrorist attacks at the World Trade Center site.

Family members are to be notified by telephone calls and letters saying that further positive identifications are not expected, leaving more than four out of 10 families with no recovered remains for burial.

But the medical examiner's office says if new DNA technology emerges, the process could easily resume.

"We've exhausted all the DNA technology as it exists today," Ellen Barakove, a spokeswoman for the medical examiner, told CNN Tuesday. "We are pausing."

For some time, the process has been at a near standstill. Of the 2,749 people known to have been killed at the World Trade Center site, only 1,585 -- or 58 percent -- were identified on the basis of recovered physical remains.

The death toll does not include the 10 hijackers who crashed passenger jets into the twin towers. Two of their remains were identified.

The medical examiner's office received a total of 19,916 human remains, which included fewer than 300 intact bodies or torsos. It identified 10,190 body parts, some as small as a finger tip, primarily through DNA testing. About 9,726 remains remain unidentified.

"The identifications have slowed up considerably over that last year or so," Barakove said.

Victims' families have made their preferences known to Medical Examiner Charles Hirsch over the past few years -- to be notified each time a remain is identified, not be notified of further remains, or to be notified only at the end of the process, which is now.

"Everyone will be getting a letter," Barakove said. "I wouldn't consider this permanent. Dr. Hirsch has made a promise to the families -- we will never stop trying."

Bill Doyle, whose 25-year-old son, Joey, was a Cantor Fitzgerald broker killed in the World Trade Center's north tower, said he has received word about the process coming to an end.

"It's three-and-half years later, and it's a mystery where my son is," Doyle said. "You don't even have a fragment."

Diane Horning, mother of Matthew Horning, a 26-year-old technology analyst for insurer Marsh & McLennan killed in the north tower, has also been notified.

Horning leads World Trade Center Families for Proper Burial, which was formed out of concern that human remains may have been mixed with building materials trucked from Ground Zero to Fresh Kills landfill in Staten Island.

She informed families in an e-mail that identifications have reached the point where no further identifications can be made "under current technology."

"The ME's office will be keeping all records and will contact families should technology enable more identifications in the future," Horning wrote.

The WTC remains were originally stored in four huge refrigerated trucks near the medical examiner's office in midtown Manhattan, but they have been dried and sealed in deterioration-proof pouches.

The "Reflecting Absence" memorial plan selected for the World Trade Center site calls for the interment of unidentified human remains at the site's deepest point, 70 feet underground, in a sort of walk-in mausoleum.

"We will have access," Barakove said. "We don't know what might come down the road whereby we might be able to make identifications, extracting DNA in a different way."